Learning the ability to generalize knowledge between similar contexts is particularly important in medical imaging as data distributions can shift substantially from one hospital to another, or even from one machine to another. To strengthen generalization, most state-of-the-art techniques inject knowledge of the data distribution shifts by enforcing constraints on learned features or regularizing parameters. We offer an alternative approach: Learning from Privileged Medical Imaging Information (LPMII). We show that using some privileged information such as tumor shape or location leads to stronger domain generalization ability than current state-of-the-art techniques. This paper demonstrates that by using privileged information to predict the severity of intra-layer retinal fluid in optical coherence tomography scans, the classification accuracy of a deep learning model operating on out-of-distribution data improves from $0.911$ to $0.934$. This paper provides a strong starting point for using privileged information in other medical problems requiring generalization.